We consider a general class of nonzero-sum N -player stochastic games with impulse controls, where players control the underlying dynamics with discrete interventions. We adopt a verification approach and provide sufficient conditions for the Nash equilibria (NEs) of the game. We then consider the limit situation of N → ∞, that is, a suitable mean-field game (MFG) with impulse controls. We show that under appropriate technical conditions, the MFG is an -NE approximation to the N -player game, with = O 1 √ N . As an example, we analyze in details a class of stochastic games which extends the classical cash management problem to the game setting. In particular, we characterize the NEs for its two-player case and compare the results to the single-player case, showing the impact of competition on the player's optimal strategy, with sensitivity analysis of the model parameters.

Background: Acute mesenteric ischemia (AMI) is a life-threatening medical condition that occurs when a sudden decreased perfusion to the intestines which leads to bowel infarction, and acute superior mesenteric artery embolism (ASMAE) is the main cause of AMI. Unfortunately, with the improvement of diagnosis and treatment technology, the mortality remains high due to less frequent clinical suspicion resulted from the unclear clinical manifestation and non-specific laboratory findings. Methods: Relevant studies published were identified by searching the PubMed, Embase and Cochrane Library databases. This review presented the literatures to introduce the research progress of ASMAE in recent years. Results: Patients with the history of atrial fibrillation, heart valve disease and atherosclerosis should be considered as ASMAE. Laboratory findings are insensitive and unspecific, however, angiography and Computed tomography angiography (CTA) can provide a clear diagnosis sensitively and specifically. Endovascular approaches have been increasingly reported in multiple case series. The key to successful treatment of AMI involves early clinical recognition and early intervention to move the embolus, which can reduce the rate of misdiagnosis and save the precious time and lives of patients. Conclusions: Loss of time eventually leads to progression of ischemia to transmural bowel necrosis with peritonitis and septicemia, which may further worsen patients’ outcomes. It is important for physicians to make a timely and accurate diagnosis, which can save precious time and reduce the mortality.

We consider a general class of nonzero-sum N-player stochastic games with impulse controls, where players control the underlying dynamics with discrete interventions. We adopt a verification approach and provide sufficient conditions for the Nash equilibria (NEs) of the game. We then consider the limiting situation when N goes to infinity, that is, a suitable mean-field game (MFG) with impulse controls. We show that under appropriate technical conditions, there exists a unique NE solution to the MFG, which is an ϵ-NE approximation to the N-player game, with [Formula: see text]. As an example, we analyze in detail a class of two-player stochastic games which extends the classical cash management problem to the game setting. In particular, we present numerical analysis for the cases of the single player, the two-player game, and the MFG, showing the impact of competition on the player’s optimal strategy, with sensitivity analysis of the model parameters.